[MUSIC] Continuing this distributional approach to evaluating managers, I quote you this quotation from a fund manager who says that there are three sides in any investment. There's the risk profile, there's a strategy and performance. And he says for a long time people have uniquely focused on performance to select funds. But this is strange, because the manager can control only two things out of three. He can control his strategy and he can control his risk profile. The uncontrollable side is performance. So we focused on delivering a desired risk profile within a given investment universe and the we got performance as a side effect. And I think that's the idea that you should be taking away from this exercise for this module. We've focused on risk profiles and we've tried to put together risk profiles that are robust and are likely to lead to future group defaults. I want to leave you with a few more tools. I want to give you some tools because they follow up on this distributional approach to evaluating fund performance. And you will see them in practical life. The most common and possibly the most abused ratio is the Sharpe ratio. But let's first understand why volatility, truly understand why volatility is a proxy for risk. Here are two possible strategies, possible investments. And you can see their distributions and their expected returns. You make an investment because you want the expected return that's why you invest in something. Now the problem is that the wider the distribution, the higher the risk that you get something other than the expected return. Maybe positive, maybe negative. But the odds are that it will be quite different from the expected return. Why is volatility a proxy for risk? Volatility is a proxy for risk because it is a measure of the distribution width. If the distribution is quite wide, then there's a high probability of getting a return which is substantially away from the expected. Since you entered the investment precisely to get the expected value. The risk is in fact the probability that you get something far away from the expectation. It really has nothing to do so much with the noisiness of returns. Technically, you just don't care about that, you just care about your final return. But the standard deviation tells you a lot about how far away from the expected return. Back to definitions, one is the Sharpe ratio. Sharpe ratio's simply the expected excess return divided by the excess volatility. If we expect over another rate typically the [INAUDIBLE] rate divided by the [INAUDIBLE] of the investment. It's very useful and can tell you some things. It can tell you that picture of something similar to the pictures that we've just seen. But don't get married to it, as we now discuss there are a few faults. What people really care about is the downside risk, the probability of getting much less than the expected return. People don't really care about upside volatility. By and large upside volatility is a good thing. So when you look at standard deviations, you're looking at things in a symmetrical matter. Both upside volatility, as well as downside volatility [INAUDIBLE]. But the reality is you don't really care about upside volatility, in fact upside volatility is a good thing. And you wouldn't care about downside risk. And one way to measure downside risk is to focus on drawdowns. Drawdown is the amount investment for it tapers off from its previous high. The Sortino ratio looks at downside risk. Very similar to the Sharpe ratio. The numerator is the same. But the denominator is now downside risk, appropriately skipped. So what the Sortino Ratio is trying to do, it's trying to differentiate between good volatility which is upside volatility and bad volatility. And so there's some attractiveness to this measure. But in doing so, the Sortino ratio, it actually ignores risk which are latent. Just because you got a good outcome doesn't mean you didn't take a lot of risk. And so that's the inherent flaw in the Sortino ratio. One more concept which you've already been introduced to and I'm looking at past historic data is to be aware of survivorship bias. The financial industry is rife with survivorship bias. You need to be on guard to make sure that the data is properly adjusted survivorship bias. Another ratio that you may come across is the Treynor ratio. Very similar to the Sharpe Ratio, but instead it uses the academic definition of Beta in the denominator instead of volatility. And so as beta equals correlation times the ratio of volatilities. The Treynor ratio is saying that investors value not just low volatility, but also low correlation. For benchmark relative strategies, like mutual funds or fund managers are trying to beat the S&P 500. A common ratio is the information ratio. It is the expected strategy return minus the benchmark return over the volatility of the difference between the two. And lastly, I'm just going to mention of few more ratios because you would come across to the some point in your careers. The Calmar ratio, the Sterling ratio, the Burke ratio. And all of these are variations to a theme to address some of the throwbacks in each of this specific ratios we have seen so far. Is there a best ratio? Unfortunately there is no best ratio. They all offer some insight, but none of them are for a magic bullet. These are all summary statistics, they all suffer from the same flaws as a summary does. Ratios and quantitative measures in general are just one tool that should be in an investor's toolbox. And importantly, there are never substitutes for a deep understanding for a manager strategy and the risks that are taken. [MUSIC]